A Game-Theoretic Approach to Self-Stabilization with Selfish Agents

TL;DR

This paper introduces a game-theoretic framework for ensuring self-stabilization in distributed multi-agent systems with selfish agents, using probabilistic strategies and fault-containment to maintain convergence and closure.

Contribution

It formulates self-stabilization as a stochastic Bayesian game and proposes new algorithms that handle selfish behaviors to ensure system stability.

Findings

Algorithms effectively handle selfish deviations.

Proposed methods outperform existing schemes.

System maintains stability despite unauthorized actions.

Abstract

Self-stabilization is an excellent approach for adding fault tolerance to a distributed multi-agent system. However, two properties of self-stabilization theory, convergence and closure, may not be satisfied if agents are selfish. To guarantee convergence, we formulate the problem as a stochastic Bayesian game and introduce probabilistic self-stabilization to adjust the probabilities of rules with behavior strategies. This satisfies agents' self-interests such that no agent deviates the rules. To guarantee closure in the presence of selfish agents, we propose fault-containment as a method to constrain legitimate configurations of the self-stabilizing system to be Nash equilibria. We also assume selfish agents as capable of performing unauthorized actions at any time, which threatens both properties, and present a stepwise solution to handle it. As a case study, we consider the problem of distributed clustering and propose five self-stabilizing algorithms for forming clusters. Simulation results show that our algorithms react correctly to rule deviations and outperform comparable schemes in terms of fairness and stabilization time.